Generating images according to points of intersection for integer multiples of a sample-time distance

ABSTRACT

According to one embodiment, generating images according to intersection points includes obtaining samples of signals from transmitter-receiver pairs. A transmitter-receiver pair is configured to transmit a signal and receive the signal reflected by an object. Intersection points are determined, where an intersection point indicates an intersection for integer multiples of a sample-time distance. A subset of samples corresponding to the intersection points is selected. Image data is generated from the selected subset of samples, where the image data is used to generate an image of the object.

TECHNICAL FIELD

This invention relates generally to the field of imaging systems andmore specifically to generating images according to points ofintersection for integer multiples of a sample-time distance.

BACKGROUND

Imaging systems generate images of objects. An imaging system typicallyreceives signals reflected from an object and generates an image of thatobject from the reflected signals. Certain imaging devices may generateimages of objects that are on the other side of a barrier. Some of thesedevices, however, cannot generate clear images of the object.

SUMMARY OF THE DISCLOSURE

In accordance with the present invention, disadvantages and problemsassociated with previous techniques for generating images may be reducedor eliminated.

According to one embodiment, generating images according to intersectionpoints includes obtaining samples of signals from transmitter-receiverpairs. A transmitter-receiver pair is configured to transmit a signaland receive the signal reflected by an object. Intersection points aredetermined, where an intersection point indicates an intersection forinteger multiples of a sample-time distance. A subset of samplescorresponding to the intersection points is selected. Image data isgenerated from the selected subset of samples, where the image data isused to generate an image of the object.

Certain embodiments of the invention may provide one or more technicaladvantages. A technical advantage of one embodiment may be that an imageis generated from samples that correspond to points of intersection forinteger multiples of a sample-time distance. The points of intersectionidentify samples that traveled an integer multiple of a sample-timedistance, where the sample-time distance is the distance that a signaltravels during a sample period. Generating an image from these samplesmay allow for improvement of the quality of an image derived from thesamples.

Certain embodiments of the invention may include none, some, or all ofthe above technical advantages. One or more other technical advantagesmay be readily apparent to one skilled in the art from the figures,descriptions, and claims included herein.

BRIEF DESCRIPTION OF THE DRAWINGS

For a more complete understanding of the present invention and itsfeatures and advantages, reference is now made to the followingdescription, taken in conjunction with the accompanying drawings, inwhich:

FIG. 1 illustrates an embodiment of an imaging system configured togenerate images according to points of intersection for integermultiples of a sample-time distance;

FIGS. 2A through 2C illustrate one embodiment of a method forcalculating intersection points for an example arrangement of atransmitter and receivers;

FIGS. 3A and 3B illustrate examples of intersection points translatedinto a Cartesian space;

FIGS. 4A and 4B illustrate an example of valid combinationscorresponding to the example arrangement of the transmitter andreceivers of FIGS. 2A through 2C; and

FIGS. 5A and 5B illustrate examples of boundaries that may beestablished for valid array points.

DETAILED DESCRIPTION OF THE DRAWINGS

Embodiments of the present invention and its advantages are bestunderstood by referring to FIGS. 1 through 5B of the drawings, likenumerals being used for like and corresponding parts of the variousdrawings.

FIG. 1 illustrates an embodiment of an imaging system 10 configured togenerate images according to points of intersection for integermultiples of a sample-time distance. Imaging system 10 generates animage 12 of object 14, which may be behind an obstruction 16. In theembodiment, imaging system 10 generates image 12 from samples thatcorrespond to points of intersection for integer multiples of asample-time distance. The intersection points of intersection identifysamples that traveled an integer multiple of a sample-time distance,where the sample-time distance is the distance that a signal travelsduring a sample period. The intersection points may be used to associatesignal sample values with image space points.

Object 14 represents any suitable physical object that can reflectsignals. In the illustrated embodiment, a signal is reflected from apoint 15 of that object. In general, signals are reflected from multiplepoints 15 of object 14. Each reflected signal carries image informationabout the point 15 from which it was reflected. Image informationderived from the multiple signals may be used to generate image 12 ofobject 14.

Image 12 represents a visual (such as optical) representation of object14. Image 12 may comprise one or more images, for example, a stillphotograph or a sequence of images that form a movie or video. Image 12may have two or three spatial dimensions. Image 12 includes image unitsthat form image 12 in Cartesian space. A pixel is a two-dimensionalimage unit, and a voxel is a three-dimensional image unit.

Obstruction 16 represents a physical barrier that blocks one or morefrequencies of electromagnetic radiation. For example, obstruction 16blocks visible light, such that object 14 on one side of obstruction 16is not visible to a viewer on the other side. Examples of obstruction 16include a building part (such as a wall, door, or ceiling), the ground,or other physical element.

In the illustrated embodiment, imaging system 10 includes an antennaarray 20, logic 24, a memory 26, and an interface 28 coupled as shown.In general, antenna array 20 receives signals reflected from object 14,logic 24 generates image data from samples of the signals and frominformation stored in memory 26, and interface 28 displays image 12generated from the image data. In one embodiment, antenna array 20 maybe attached to a vehicle capable of moving, and may itself move withrespect to the vehicle.

Antenna array 20 includes antenna elements, where an antenna elementtransmits and/or receives a signal. When transmitting a signal, anantenna element is regarded as a transmitter 30, and when receiving asignal, an antenna element is regarded as a receiver 34. In theillustrated embodiment, antenna array 20 includes transmitter TX andreceivers RX1, RX2, RX3, and RX4.

A transmitter-receiver pair includes a transmitter that transmits asignal and a receiver that receives the signal. The signal may bereflected by an object (such as object 14 or obstruction 16) afteremission and prior to reception. In the illustrated embodiment, antennaarray 20 includes transmitter-receiver pairs TX-RX1, TX-RX2, TX-RX3, andTX-RX4. The round-trip distance for a transmitter-receiver pair is thedistance a signal travels as the signal is transmitted from transmitter30, reflected from object 14, and received by receiver 34.

In certain embodiments, transmitter 30 transmits very sharp discretepulses, as in impulsive radar. The duration of the pulse is typicallyvery short relative to the round-trip distance. Receiver 34 may samplethe received signal, and may sample the signal at a fixed sampling rate.

Antenna array 20 has any suitable number of antenna elements that formany suitable number of transmitter-receiver pairs as may be used for aparticular application. For example, antenna array 20 may have onetransmitter-receiver pair that includes one transmitter and onereceiver; two transmitter-receiver pairs that include one transmitterand two receivers, two transmitters and one receivers, or twotransmitters and two receivers; three transmitter-receiver pairs thatinclude one transmitter and three receivers or three transmitters andone receiver; four transmitter-receiver pairs that include onetransmitter and four receivers (as shown) or four transmitters and onereceiver; or more transmitter-receiver pairs.

In the illustrated embodiment, logic 24 includes a processor 40, a datacollector 44, and an image processor 48 coupled as shown. Memory 26records points 58 of intersection for integer multiples of a sample-timedistance and stores one or more lookup tables (LUTs) 60. Data collector44 receives samples of signals from receivers 34. The samples includeimage information that may be used to generate image 12 of object 14.Data collector 44 may process (such as filter) samples to allow them tobe processed by image processor 48.

In particular embodiments, image processor 48 selects samples. Eachsample corresponds to a receiver 34 of antenna array 20. Crosscombinations of the selected points correspond to points of intersectionfor integer multiples of a sample-time distance. Image processor 48performs calculations to generate image data from the selected samples.The image data is used to generate image 12. The intersection pointsidentify samples that traveled an integer multiple of a constant sampletime signal propagation distance. In the illustrated embodiment, imageprocessor 48 includes an intersection point module 50, a sample selector52, and an image generator 54 coupled as shown.

Intersection point module 50 establishes round-trip ellipsoids for eachtransmitter-receiver pair of antenna array 20, and calculates theintersection points of the intersections of the round-trip ellipsoids.In one embodiment, intersection point module 50 calculates theintersection points of the intersections of integer round-tripellipsoids.

In certain embodiments, a round-trip ellipsoid is a Fresnel ellipse orellipsoid formed from points having the same round-trip distances for atransmitter-receiver pair. In certain embodiments, a roundtrip ellipsoidis an integer multiple of a sample-time distance roundtrip ellipsoid. Inthe embodiments, sample-time distance is the distance that a signaltravels during a sample period. A roundtrip ellipsoid is formed frompoints with the same integer roundtrip distance. Examples of calculatingthe points of intersection for integer multiples of a sample-timedistance are described in more detail with reference to FIGS. 2A through2C.

Sample selector 52 selects samples corresponding to the points ofintersection for integer multiples of a sample-time distance. Sampleselector 52 may select samples by using a causal filtering function tofilter samples from receivers 34. Examples of filtering functionsinclude cross multiplication, cross summation, cross correlation,matched filter, and/or other filter function.

Image generator 54 obtains values from the selected samples and maps thevalues to image units to generate image 12. In particular embodiments,the values may represent brightness and/or color. A value may be mappedto an image unit to designate the appearance of image 12 at the imageunit.

Image generator 54 may map the values to image units in any suitablemanner. In particular embodiments, image generator 54 may determine animage unit that corresponds to an intersection point, and then may mapthe value from samples associated with the intersection point to theimage unit corresponding to the intersection point.

The image unit that corresponds to a given intersection point may bedetermined in any suitable manner. In particular embodiments, imagegenerator 54 accesses one or more lookup tables 60. In certainembodiments, a look-up table 60 may be constructed for sets of threetransmitter-receiver pairs. A look-up table 60 may be calculatedrelative to the reference frame of array 20.

In one embodiment, a lookup table 60 may map intersection points tocorresponding image units. In another embodiment, a first lookup table60 may map the intersection to points in Cartesian space, and a secondlookup table 60 may map Cartesian points to corresponding image units.In the embodiment, the Cartesian space may be a Cartesian coordinatesystem that is defined with respect to antenna array 20.

In particular embodiments, intersection points are not uniformlydistributed in Cartesian space. Accordingly, zero, one, two, or moreintersection points may correspond to a particular image unit. Examplesof generating information for lookup tables 60 is described in moredetail with reference to FIGS. 4A and 4B.

Image generator 54 may perform other suitable image generatingoperations. As an example, image generator 54 may apply a weightingfunction to account for smaller energy contributions of signals frompoints 15 farther away from transmitter 30. As another example, imagegenerator 54 may determine a specific area to be imaged, and then searcha look-up 60 table associated with that specific area.

Interface 28 displays image 12 generated from the image data. Interface28 may comprise a two- or three-dimensional display such as a screen fora computer, a helmet, and/or a television.

A component of system 10 may include an interface, logic, memory, and/orother suitable element. An interface receives input, sends output,processes the input and/or output, and/or performs other suitableoperation. An interface may comprise hardware and/or software.

Logic performs the operations of the component, for example, executesinstructions to generate output from input. Logic may include hardware,software, and/or other logic. Logic may be encoded in one or moretangible media and may perform operations when executed by a computer.Certain logic, such as a processor, may manage the operation of acomponent. Examples of a processor include one or more computers, one ormore microprocessors, one or more applications, and/or other logic.

A memory stores information. A memory may comprise one or more tangible,computer-readable, and/or computer-executable storage medium. Examplesof memory include computer memory (for example, Random Access Memory(RAM) or Read Only Memory (ROM)), mass storage media (for example, ahard disk), removable storage media (for example, a Compact Disk (CD) ora Digital Video Disk (DVD)), database and/or network storage (forexample, a server), and/or other computer-readable medium.

System 10 may be embodied as any suitable imaging system. Examples ofsuch imaging systems include a ground penetrating radar (GPR), athrough-the-wall (TTW), an impulsive radar, and an ultra-wide band (UWB)radar system. Imaging system 10 may be used for any suitableapplication, for example, buried land mine detection, imaging,subsurface inspection, and/or other suitable application.

Modifications, additions, or omissions may be made to system 10 withoutdeparting from the scope of the invention. The components of system 10may be integrated or separated. Moreover, the operations of system 10may be performed by more, fewer, or other components. For example, theoperations of sample selector 52 and image generator 54 may be performedby one component, or the operations of image generator 54 may beperformed by more than one component. Additionally, operations of system10 may be performed using any suitable logic comprising software,hardware, and/or other logic. As used in this document, “each” refers toeach member of a set or each member of a subset of a set.

FIGS. 2A through 2C illustrate one embodiment of a method forcalculating intersection points for an example arrangement oftransmitter 30 and receivers 34. In the example, transmitter 30 andreceivers 34 include transmitter TX and receivers RX1, RX2, and RX3 thatform transmitter-receiver pairs TX-RX1, TX-RX2, and TX-RX3. TransmitterTX and receivers RX1 and RX2 are co-linear.

Sample-time distance D_(s) represents the distance a signal travelsduring a sample period. In the example, receivers 34 sample signals at afixed rate F_(s). The sample-time distance D_(s)=c/F_(s), where c is thespeed of light. Integer round-trip distance L·D_(s), where L is aninteger, represents a round-trip distance that is an integer multiple ofsample-time distance D_(s).

FIG. 2A is a two-dimensional graph 210 of examples of sets 214 (214 a,b)of round-trip ellipsoids 218. Points with the same integer multiple ofthe round-trip distance form a round-trip ellipsoid 218. Eachtransmitter-receiver pair has a set 214 of such round-trip ellipsoids218. Set 214 a is for transmitter-receiver pair TX-RX1, and set 214 b isfor transmitter-receiver pair TX-RX2. A round-trip ellipsoid 218 of oneset 214 a may intersect another round-trip ellipsoid 218 of another set214 b at an intersection ellipse, such as an intersection circle 212.

In the illustrated example, receiver RX1, transmitter TX, and receiverRX2 are co-linear. Since they are co-linear, the intersection ellipse isan intersection circle. If they are not co-linear, the intersectionellipse is not a circle.

FIG. 2B is a three-dimensional graph 240 of intersection circle 212.Intersection circle 212 is the intersection of ellipsoids formed frominteger multiples of the round-trip distances from transmitter-receiverpairs TX-RX1 and TX-RX2. In the example, intersection circle 212 is:x ² +z ² =x ₀ ²In the example, receiver RX3 is at point (0, 0, H). The center ofintersection circle 212 is at (0, y₀, 0), and the radius is x₀, theplane of the circle is perpendicular to the Y axis.

FIG. 2C is a graph 250 illustrating third receiver RX3. The intersectionpoints where integer round-trip ellipses (not shown) oftransmitter-receiver pair TX-RX3 intersect intersection circle 212 maybe calculated as follows.

Distance d₁ represents the distance between transmitter TX andintersection circle 212. In the example, distance d₁ is:d ₁=sqrt(x ₀ ² +y ₀ ²)Distance d₂ represents the distance between RX3 and the intersectioncircle. Accordingly:d ₁ +d ₂ =L·D _(s)

For an arbitrary point (x, y₀, z) on the intersection circle:d ₁=√(z ² +x ² +y ₀ ²)d ₂=norm((0,0,H),(x,y ₀ ,z))=√((H−z)² +x ² +y ₀ ²)L·D _(s) =d ₁+√(H ²−2Hz+z ² +y ² +y ₀ ²)L·D _(s) =d ₁+√(H ²−2Hz+d ₁ ²)L·D _(s) =d ₁+√(H ²−2Hz+d ₁ ²)(L·D _(s) −d ₁)² =H ²−2Hz+d ₁ ²2Hz=H ² +d ₁ ²−(LD _(s) −d ₁)²2Hz=H ² +d ₁ ² −L ² D _(s) ²+2LD _(s) d ₁ −d ₁ ²

Consequently:z={H ²+2LD _(s) d ₁ −L ² D _(s) ²}/2Hwhere d ₁=√(x ₀ ² +y ₀ ²)

The radius of intersection circle 212 is x₀, so:x ² +z ² =x ₀ ²

Finally:x=√(x ₀ ² −z ²)

Given values for x₀, y₀, and H, the solution is:x=√(x ₀ ² −z ²)y=y₀z={H ²+2LD _(s) d ₁ −L ² D _(s) ²}/2Hwhere d ₁=√(x ₀ ² +y ₀ ²).

Any suitable arrangement of three transmitter-receiver pairs yield auniquely determined set of points of intersection for integer multiplesof a sample-time distance. The set may include one transmitter and threereceivers or three transmitters and one receiver.

In certain cases, there is not necessarily a unique set of intersectionpoints. For example, if a fourth receiver is added, there is notnecessarily a unique set of points. In these cases, the antenna elementsmay be decomposed into subsets of three transmitter-receiver pairs, orsub-arrays. A 3-space image may be constructed using any of thesesubsets. An image constructed from a particular subset may be referredto as a view. A composite image may be formed by combining multipleviews.

Modifications, additions, or omissions may be made to the method withoutdeparting from the scope of the invention. The method may include more,fewer, or other steps. Additionally, steps may be performed in anysuitable order.

FIGS. 3A and 3B illustrate intersection points translated into Cartesianspace. The points may be translated into any suitable Cartesian spacesuch as a Cartesian coordinate system in the frame of reference of array20. The intersection points in Cartesian space indicate validcombinations of indices representing receivers 34.

FIG. 3A is a graph 310 of points 314 of intersection for integermultiples of a sample-time distance plotted on an xy plane. In theexample, intersection points 314 are shown to be non-uniformlydistributed. The arrangement (including density) of points 314 is afunction of the placement of transmitters 30 and receivers 34, as wellas the sampling frequency.

FIG. 3B illustrates graph 310 at a smaller scale. Graph 310 includescells 318 of the xy plane. In the example, certain cells 318 have apoint 314 relatively close to the center of cell 318, other cells 318have a point 314 at the edge of the cell 318, and yet other cells 318have no points 314.

FIGS. 4A and 4B illustrate valid combinations for example receivers 34.In the example, index k represents integer values for receiver RX1,index 1 represents integer values for receiver RX2, and index mrepresents integer values for receiver RX3.

FIG. 4A is a graph 410 illustrating valid combinations for indices k, 1,and m=900. FIG. 4B is a graph 420 illustrating valid combinations forindices k and 1 and various values of m. Graphs 410 and 420 indicatethat the valid combinations are limited. Accordingly, array pointscorresponding to the combinations may be bounded. Bounding the arraypoints limits the number of points of intersection for integer multiplesof a sample-time distance, which in turn limits the values calculatedcorresponding to the intersection points. Array points may be bounded byfiltering signals from array 20.

FIGS. 5A and 5B illustrate examples of such boundaries for array points.Any suitable boundary may be used. In general, a boundary that mostaccurately captures the points may be more complicated to calculate.

FIG. 5A is a graph 510 illustrating a tight boundary 514. Tight boundary514 may require a complex set of boundary checks. FIG. 5B is a graph 520illustrating a k×1 filtering boundary 524, a diagonal filtering boundary528, and a polygonal boundary 532. K×1 filtering boundary 524 may becalculated from a cross multiplication of two specifically sizedvectors. Diagonal filtering boundary 528 may be implemented by diagonalfiltering. Polygonal boundary 532 may be implemented by incrementingboundary pointers as well as boundary checks.

Certain embodiments of the invention may provide one or more technicaladvantages. A technical advantage of one embodiment may be that an imageis generated from samples that correspond to points of intersection forinteger multiples of a sample-time distance. The intersection points aresamples that traveled an integer multiple of a sample-time distance,where the sample-time distance is the distance that a signal travelsduring a sample period. Generating an image from these samples mayimprove the quality of the image.

Although this disclosure has been described in terms of certainembodiments, alterations and permutations of the embodiments will beapparent to those skilled in the art. Accordingly, the above descriptionof the embodiments does not constrain this disclosure. Other changes,substitutions, and alterations are possible without departing from thespirit and scope of this disclosure, as defined by the following claims.

1. A method comprising: obtaining a plurality of samples of a pluralityof signals from a plurality of transmitter-receiver pairs, atransmitter-receiver pair configured to transmit a signal and receivethe signal reflected by an object; identifying a plurality of integermultiples of a sample-time distance; determining with a processor, usinga logic encoded in one or more non-transitory computer-executablestorage media, a plurality of intersection points, an intersection pointindicating an intersection for the identified plurality of integermultiples of the sample-time distance; selecting a subset of samplescorresponding only to the intersection points; and generating image datafrom the selected subset of samples, the image data used to generate animage of the object.
 2. The method of claim 1, further comprisingcalculating the intersection points by: for each transmitter-receiverpair, establishing a plurality of round-trip ellipsoids; and calculatingthe intersection points from a plurality of intersections of theplurality of round-trip ellipsoids.
 3. The method of claim 1, theplurality of transmitter-receiver pairs comprising threetransmitter-receiver pairs.
 4. The method of claim 1: the plurality oftransmitter-receiver pairs comprising a plurality of sets of threetransmitter-receiver pairs; and the determining the plurality ofintersection points further comprising: determining a set ofintersection points for each set of three transmitter-receiver pairs. 5.The method of claim 1, the generating the image data from the selectedsubset of samples further comprising: obtaining a plurality of valuesfrom the selected samples; and mapping the values to a plurality ofimage units of the image.
 6. The method of claim 1, the generating theimage data from the selected subset of samples further comprising:accessing one or more lookup tables that map an intersection point to acorresponding image unit.
 7. The method of claim 1, the generating theimage data from the selected subset of samples further comprising:accessing a lookup table that maps an intersection point to acorresponding Cartesian coordinate point.
 8. The method of claim 1,further comprising: filtering the signals according to the intersectionpoints.
 9. The method of claim 1, further comprising: determining anarea to be imaged; and selecting the intersection points according tothe area to be imaged.
 10. The method of claim 1, further comprising:selecting a plurality of array points according to the intersectionpoints.
 11. A system comprising logic encoded in one or morenon-transitory computer-executable storage media and when executedoperable to: obtain a plurality of samples of a plurality of signalsfrom a plurality of transmitter-receiver pairs, a transmitter-receiverpair configured to transmit a signal and receive the signal reflected byan object; and identify a plurality of integer multiples of asample-time distance determine a plurality of intersection points, anintersection point indicating an intersection for the identifiedplurality of integer multiples of the sample-time distance; select asubset of samples corresponding only to the intersection points; andgenerate image data from the selected subset of samples, the image dataused to generate an image of the object.
 12. The system of claim 11, thelogic further operable to calculate the intersection points by: for eachtransmitter-receiver pair, establishing a plurality of round-tripellipsoids; and calculating the intersection points from a plurality ofintersections of the plurality of round-trip ellipsoids.
 13. The systemof claim 11, the plurality of transmitter-receiver pairs comprisingthree transmitter-receiver pairs.
 14. The system of claim 11: theplurality of transmitter-receiver pairs comprising a plurality of setsof three transmitter-receiver pairs; and the logic further operable todetermine the plurality of intersection points by: determining a set ofintersection points for each set of three transmitter-receiver pairs.15. The system of claim 11, the logic further operable to generate theimage data from the selected subset of samples by: obtaining a pluralityof values from the selected samples; and mapping the values to aplurality of image units of the image.
 16. The system of claim 11, thelogic further operable to generate the image data from the selectedsubset of samples by: accessing one or more lookup tables that map anintersection point to a corresponding image unit.
 17. The system ofclaim 11, the logic further operable to generate the image data from theselected subset of samples by: accessing a lookup table that maps anintersection point to a corresponding Cartesian coordinate point. 18.The system of claim 11, the logic further operable to: filter thesignals according to the intersection points.
 19. The system of claim11, the logic further operable to: determine an area to be imaged; andselect the intersection points according to the area to be imaged. 20.The system of claim 11, the logic further operable to: select aplurality of array points according to the intersection points.
 21. Asystem comprising logic encoded in one or more non-transitorycomputer-executable storage media and when executed operable to: obtaina plurality of samples of a plurality of signals from a plurality oftransmitter-receiver pairs, a transmitter-receiver pair configured totransmit a signal and receive the signal reflected by an object, theplurality of transmitter-receiver pairs comprising a plurality of setsof three transmitter-receiver pairs; calculate a plurality ofintersection points by: for each transmitter-receiver pair, establishinga plurality of round-trip ellipsoids; and calculating the intersectionpoints from a plurality of intersections of the plurality of round-tripellipsoids; identify a plurality of integer multiples of a sample-timedistance; determine the intersection points, an intersection pointindicating an intersection for the identified plurality of integermultiples of the sample-time distance, by: determining a set ofintersection points for each set of three transmitter-receiver pairs;select a subset of samples corresponding only to the intersectionpoints; and generate image data from the selected subset of samples, theimage data used to generate an image of the object, by: obtaining aplurality of values from the selected samples; accessing one or morelookup tables that map an intersection point to a corresponding imageunit; and mapping the values to a plurality of image units of the image.